set A = { P where P is Subset of (REAL n) : ex x1, x2, x3 being Element of REAL n st P = plane x1,x2,x3 } ;
{ P where P is Subset of (REAL n) : ex x1, x2, x3 being Element of REAL n st P = plane x1,x2,x3 } c= bool (REAL n)

proof

let P be set ; :: according to TARSKI:def 3 :: thesis: ( not P in { P where P is Subset of (REAL n) : ex x1, x2, x3 being Element of REAL n st P = plane x1,x2,x3 } or P in bool (REAL n) )
assume P in { P where P is Subset of (REAL n) : ex x1, x2, x3 being Element of REAL n st P = plane x1,x2,x3 } ; :: thesis: P in bool (REAL n)
then consider P' being Subset of (REAL n) such that
A1: ( P = P' & ex x1, x2, x3 being Element of REAL n st P' = plane x1,x2,x3 ) ;
thus P in bool (REAL n) by A1; :: thesis: verum

end;

hence { P where P is Subset of (REAL n) : ex x1, x2, x3 being Element of REAL n st P = plane x1,x2,x3 } is Subset-Family of (REAL n) ; :: thesis: verum